{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[第一章]\n",
    "\n",
    "## 最小二乘法\n",
    "\n",
    "高斯于1823年在误差e1 ,… , en独立同分布的假定下,证明了最小二乘方法的一个最优性质: 在所有无偏的线性估计类中,最小二乘方法是其中方差最小的！"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用最小二乘法拟和曲线\n",
    "\n",
    "对于数据$(x_i, y_i)(i=1, 2, 3...,m)$\n",
    "\n",
    "拟合出函数$h(x)$\n",
    "\n",
    "有误差，即残差：$r_i=h(x_i)-y_i$\n",
    "\n",
    "此时L2范数(残差平方和)最小时，h(x) 和 y 相似度最高，更拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一般的H(x)为n次的多项式，$H(x)=w_0+w_1x+w_2x^2+...w_nx^n$\n",
    "\n",
    "$w(w_0,w_1,w_2,...,w_n)$为参数\n",
    "\n",
    "最小二乘法就是要找到一组 $w(w_0,w_1,w_2,...,w_n)$ 使得$\\sum_{i=1}^n(h(x_i)-y_i)^2$ (残差平方和) 最小\n",
    "\n",
    "即，求 $min\\sum_{i=1}^n(h(x_i)-y_i)^2$\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "举例：我们用目标函数$y=sin2{\\pi}x$, 加上一个正太分布的噪音干扰，用多项式去拟合【例1.1 11页】"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from scipy.optimize import leastsq\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*ps: numpy.poly1d([1,2,3])  生成  $1x^2+2x^1+3x^0$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 目标函数\n",
    "def real_func(x):\n",
    "    return np.sin(2*np.pi*x)\n",
    "\n",
    "# 多项式\n",
    "def fit_func(p, x):\n",
    "    f = np.poly1d(p)\n",
    "    return f(x)\n",
    "\n",
    "# 残差\n",
    "def residuals_func(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 十个点\n",
    "x = np.linspace(0, 1, 10)\n",
    "x_points = np.linspace(0, 1, 1000)\n",
    "# 加上正态分布噪音的目标函数的值\n",
    "y_ = real_func(x)\n",
    "y = [np.random.normal(0, 0.1)+y1 for y1 in y_]\n",
    "\n",
    "def fitting(M=0):\n",
    "    \"\"\"\n",
    "    n 为 多项式的次数\n",
    "    \"\"\"    \n",
    "    # 随机初始化多项式参数\n",
    "    p_init = np.random.rand(M+1)\n",
    "    # 最小二乘法\n",
    "    p_lsq = leastsq(residuals_func, p_init, args=(x, y))\n",
    "    print('Fitting Parameters:', p_lsq[0])\n",
    "    \n",
    "    # 可视化\n",
    "    plt.plot(x_points, real_func(x_points), label='real')\n",
    "    plt.plot(x_points, fit_func(p_lsq[0], x_points), label='fitted curve')\n",
    "    plt.plot(x, y, 'bo', label='noise')\n",
    "    plt.legend()\n",
    "    return p_lsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-0.00617663]\n"
     ]
    },
    {
     "data": {
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bJTMyQGvzY0JC7YpAeno67du357777qNDhw4MHTqUoqIidu7cSa9evYiOjuamm27izJkz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e6a7c5e2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=0\n",
    "p_lsq_0 = fitting(M=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [-1.30171899  0.64468286]\n"
     ]
    },
    {
     "data": {
      "image/png": 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i8m0W7kkwNBYhLMUhE8C5a8nM232OJ+sHEFjcRss926rSodDlc31U0OULUE6w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\ncJYoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e6a7c35cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=1\n",
    "p_lsq_1 = fitting(M=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [ 21.71234993 -32.65844254  11.14547436  -0.11918864]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Cq5fj02XhpGfJnAFCSAK44MLD36rNeW+bMx6uzjx9Vx2zoxIF5VkFerwDkWux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\nBhARMVBpABERA/UL2yQSR1sNFVsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e6ab165d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=3\n",
    "p_lsq_3 = fitting(M=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting Parameters: [ -1.44528174e+04   6.21907672e+04  -1.11295017e+05   1.07136020e+05\n",
      "  -5.98785140e+04   1.95471674e+04  -3.53973846e+03   2.92993167e+02\n",
      "  -7.29804911e-01  -9.13396601e-02]\n"
     ]
    },
    {
     "data": {
      "image/png": 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mlJq4bxEEtzY7PFEGKQdtf9aWg5Y7gAowceLlF3+AnBzFxInGhC7j5mzjTHYBH9/TTi7+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\nLkoSgBBCuChJAEII4aL+H4iwJmBHYDvpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e6ab4f79e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# M=9\n",
    "p_lsq_9 = fitting(M=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当M=9时，多项式曲线通过了每个数据点，但是造成了过拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 正则化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果显示过拟合， 引入正则化项(regularizer)，降低过拟合\n",
    "\n",
    "$Q(x)=\\sum_{i=1}^n(h(x_i)-y_i)^2+\\lambda||w||^2$。\n",
    "\n",
    "回归问题中，损失函数是平方损失，正则化可以是参数向量的L2范数,也可以是L1范数。\n",
    "\n",
    "- L1: regularization\\*abs(p)\n",
    "\n",
    "- L2: 0.5 \\* regularization \\* np.square(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "regularization = 0.0001\n",
    "\n",
    "def residuals_func_regularization(p, x, y):\n",
    "    ret = fit_func(p, x) - y\n",
    "    ret = np.append(ret, np.sqrt(0.5*regularization*np.square(p))) # L2范数作为正则化项\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 最小二乘法,加正则化项\n",
    "p_init = np.random.rand(9+1)\n",
    "p_lsq_regularization = leastsq(residuals_func_regularization, p_init, args=(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e6ab14c0f0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/wrggcr9s/pHuaWo/H3IKi9hnNoonMzLZGrmDcynn1I4lVSUJYcZ2+7K2/4O8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\nAE3TNA+lGwBN0zQPpRsATdM0D/X/rS7mO2aYMU0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e6ab527e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_points, real_func(x_points), label='real')\n",
    "plt.plot(x_points, fit_func(p_lsq_9[0], x_points), label='fitted curve')\n",
    "plt.plot(x_points, fit_func(p_lsq_regularization[0], x_points), label='regularization')\n",
    "plt.plot(x, y, 'bo', label='noise')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
